Michael Brown's donation was the Lib Dem's biggest ever
Police are looking into money laundering allegations over the Liberal Democrats' acceptance of £2.4m from a donor later convicted of fraud.
Michael Brown's donation hugely boosted the party's 2005 election campaign, the BBC's Newsnight programme said.
Mr Brown was convicted of fraud in 2008 but vanished before being sentenced to seven years in jail last month.
The party said its auditors were "satisfied that we do not need to make provision for repayment".
Mr Brown's victims say the Liberal Democrats were using their stolen money.
Now one of them, Robert Mann, who is already suing the party to get it back, has instructed his lawyers to ask police to investigate whether the party breached the 2002 Proceeds of Crime Act.
Mr Mann, himself a tax lawyer in California, told Newsnight: "The money was used by Mr Brown for something totally opposite to what the purpose of the investment was.
One of Michael Brown's victims, Robert Mann: "These monies belong to me"
"The monies, as we found out, or a big part of them, wound up with the Liberal Democrats, and in my mind anybody that did even a modicum of checking would have known that these monies belonged to me and not to Mr Brown.
"It's absolutely shocking how any major political party or any political party in England wouldn't want to return monies that are clearly stolen, absolutely traceable to me personally, and the individual that gave them the money is now a convicted felon."
City of London Police have confirmed to Newsnight that they have received a complaint against the Liberal Democrats and are still looking into it.
They hope to speak to Mr Mann and his lawyers shortly before deciding whether to launch a full investigation.
The head of the economic crime unit, detective chief superintendent Stephen Head, said: "On the face of it they seem to be serious allegations."
A spokesman for the Liberal Democrats said: "All our donations from 5th Avenue Partners were received in good faith and were properly spent on the general election campaign.
"Our auditors have seen our legal advice on this matter and are satisfied that we do not need to make provision for repayment."
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